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4.2.4 Modular Integers

Let A and B be integers. The expression A%B has type ZMOD and represents the class of A modulo B. The integer B should be greater than 0 and less then 32767 = 2^{15} - 1.

When a modular integer is evaluated by CoCoA, it is reduced to a canonical form A%B with -B/2 < A <= B/2.

Two modular integers of the form A%C and B%C are said to be compatible, and the usual arithmetical operations are applicable.

example

    
3%7;
3 % 7
-------------------------------
4%7;
-3 % 7
-------------------------------
2%5 + 4%5;
1 % 5
-------------------------------
Type(3%11);
ZMOD
-------------------------------
3%11 = 14%11;
TRUE
-------------------------------
3%11 = 3;
FALSE
-------------------------------
        
    
Use the functions Div and Mod for quotients and remainders.